To solve the equation \(x^2 + 10x - 16 = 0\) using factoring, we first rewrite the quadratic equation in the standard form.
The equation is already in standard form: \[ x^2 + 10x - 16 = 0. \]
Next, we need to factor it. We are looking for two numbers that multiply to \(-16\) (the constant term) and add up to \(10\) (the coefficient of the linear term).
The two numbers that satisfy this condition are \(12\) and \(-2\), since: \[ 12 \times (-2) = -24, \] and \[ 12 + (-2) = 10. \]
Thus, we can rewrite the equation as: \[ (x + 12)(x - 2) = 0. \]
Putting it in the requested form, we should enter: \[ (x + (-2))(x + 12) = 0. \]
So the final answer is: \[ (x - 2)(x + 12) = 0. \]
Thus, the numbers to fill in the blanks are: \(-2\) and \(12\).
So, your answer is: \((x - 2)(x + 12) = 0.\)